Determine size of planet's core by distance S-waves travel

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The discussion revolves around determining the size and nature of a planet's core based on S-wave travel distances. S-waves, which cannot travel through liquid, were detected at -60 degrees latitude after a seismic event, indicating that the core may be solid or partially solid. The question arises about the possibility of an off-center core affecting S-wave propagation. Participants express confusion about the S-wave detection pattern and seek clarification on seismic wave behavior in relation to the planet's structure. Understanding these factors is crucial for accurately assessing the planet's core characteristics.
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You are visiting a new planet with radius of 5000km. You set up a seismic network and detonate a test chare at the north pole at time T=0. At time T=24minutes your instruments detect S-waves at a latitude of -60 degrees. No S-waves are detected south of -60 degrees.

what is the size and nature of the planet's core?


So, I know S-waves can't penetrate liquid, but they do not travel linearly because they refract through different density layers. However, I don't understand why the S-waves travel all the way down to -60 degrees. Can a planet have a core that is off center? I don't really know where to start, any help would be appreciated
 
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